Regularity of elliptic and parabolic systems

Authors:
  • TCTobias Holck Colding
    Tobias Holck Colding
  • WIWilliam P. Minicozzi Ii
    William P. Minicozzi Ii
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Abstract
We show uniqueness of cylindrical blowups for mean curvature flow in all dimension and all codimension. Mean curvature flow in higher codimension is a nonlinear parabolic system whose complexity increases as the codimension increases. Our results imply regularity of the singular set for the system.